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**Aristaeus the Elder** (Greek : Ἀρισταῖος ὁ Πρεσβύτερος; 370 – 300 BC) was a Greek mathematician who worked on conic sections. He was a contemporary of Euclid.

**Greek** is an independent branch of the Indo-European family of languages, native to Greece, Cyprus and other parts of the Eastern Mediterranean and the Black Sea. It has the longest documented history of any living Indo-European language, spanning more than 3000 years of written records. Its writing system has been the Greek alphabet for the major part of its history; other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic, and many other writing systems.

The **Greeks** or **Hellenes** are an ethnic group native to Greece, Cyprus, southern Albania, Italy, Turkey, Egypt and, to a lesser extent, other countries surrounding the Mediterranean Sea. They also form a significant diaspora, with Greek communities established around the world.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Only little is known of his life. The mathematician Pappus of Alexandria refers to him as Aristaeus the Elder. Pappus gave Aristaeus great credit for a work entitled *Five Books concerning Solid Loci* which was used by Pappus but has been lost. He may have also authored the book *Concerning the Comparison of Five Regular Solids*. This book has also been lost; we know of it through a reference by the Greek mathematician Hypsicles.

**Pappus of Alexandria** was one of the last great Greek mathematicians of Antiquity, known for his *Synagoge* (Συναγωγή) or *Collection*, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than, that he had a son named Hermodorus, and was a teacher in Alexandria.

**Hypsicles** was an ancient Greek mathematician and astronomer known for authoring *On Ascensions* (Ἀναφορικός) and the Book XIV of Euclid's *Elements*. Hypsicles lived in Alexandria.

Heath 1921 notes, "Hypsicles (who lived in Alexandria) says also that Aristaeus, in a work entitled *Comparison of the five figures*, proved that the same circle circumscribes both the pentagon of the dodecahedron and the triangle of the icosahedron inscribed in the same sphere; whether this Aristaeus is the same as the Aristaeus of the Solid Loci, the elder contemporary of Euclid, we do not know."^{ [1] }

**Diophantus of Alexandria** was an Alexandrian Hellenistic mathematician, who was the author of a series of books called *Arithmetica*, many of which are now lost. Sometimes called "the father of algebra", his texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' *Arithmetica,* Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as *adaequalitas* in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.

**Euclid**, sometimes given the name **Euclid of Alexandria** to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.

**Euclidean geometry** is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the *Elements*. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The *Elements* begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the *Elements* states results of what are now called algebra and number theory, explained in geometrical language.

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).

**Menelaus of Alexandria** was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.

The * Elements* is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.

**Sir Thomas Little Heath** was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.

**Apollonius of Perga** was a Greek geometer and astronomer known for his theories on the topic of conic sections. Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today.

**Theon of Alexandria** was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's *Elements* and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

**Ctesibius** or **Ktesibios** or **Tesibius** was a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt. He wrote the first treatises on the science of compressed air and its uses in pumps. This, in combination with his work on the elasticity of air *On pneumatics*, earned him the title of "father of pneumatics." None of his written work has survived, including his *Memorabilia,* a compilation of his research that was cited by Athenaeus. Ctesibius' most commonly known invention today is a pipe organ (hydraulis), on which the invention of the piano was later based.

**Hippasus of Metapontum**, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus by name or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, which is believed to have been discovered around the time that he lived.

**Autolycus of Pitane** was a Greek astronomer, mathematician, and geographer. The lunar crater Autolycus was named in his honour.

**Greek mathematics** refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the Ancient Greek: μάθημα, translit. *máthēma*Attic Greek: [má.tʰɛː.ma]Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key difference between Greek mathematics and those of preceding civilizations.

A **porism** is a mathematical proposition or corollary. In particular, the term **porism** has been used to refer to a direct result of a proof, analogous to how a corollary refers to a direct result of a theorem. In modern usage, a **porism** is a relation that holds for an infinite range of values but only if a certain condition is assumed, for example Steiner's porism. The term originates from three books of Euclid with porism, that have been lost. Note that a proposition may not have been proven, so a porism may not be a theorem, or for that matter, it may not be true.

**Theodosius of Bithynia** was a Greek astronomer and mathematician who wrote the *Sphaerics*, a book on the geometry of the sphere.

**Greek astronomy** is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as **Hellenistic astronomy**, while the pre-Hellenistic phase is known as **Classical Greek astronomy**. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.

**Carpus of Antioch** was an ancient Greek mathematician. It is not certain when he lived; he may have lived any time between the 2nd century BC and the 2nd century AD. He wrote on mechanics, astronomy, and geometry. Proclus quotes from an *Astronomical Treatise* by Carpus concerning whether problems should come before theorems, in which Carpus may have been criticising Geminus. Proclus also quotes the view of Carpus that "an angle is a quantity, namely a distance between the lines of surfaces containing it." According to Pappus, Carpus made use of mathematics for practical applications. According to Iamblichus, Carpus also constructed a curve for the purpose of squaring the circle, which he calls a curve generated by a double motion.

**Basilides of Tyre** was a mathematician, mentioned by Hypsicles in his prefatory letter of Euclid's Elements, Book XIV. Barnes and Brunschwig suggested that Basilides of Tyre and Basilides the Epicurean could be the same Basilides.

- ↑ Thomas Little Heath (1908). "The thirteen books of Euclid's Elements".

- Vogel, Kurt (1970). "Aristaeus".
*Dictionary of Scientific Biography*.**1**. New York: Charles Scribner's Sons. pp. 245–246. ISBN 0-684-10114-9.

The * Dictionary of Scientific Biography* is a scholarly reference work that was published from 1970 through 1980. It is supplemented by the

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

- O'Connor, John J.; Robertson, Edmund F., "Aristaeus the Elder",
*MacTutor History of Mathematics archive*, University of St Andrews .

**Edmund Frederick Robertson** is a Professor emeritus of pure mathematics at the University of St Andrews.

The **MacTutor History of Mathematics archive** is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the history of mathematics.

The **University of St Andrews** is a British public university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy.

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